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yeah, i really need to go to school soon.
i haven't taken any sort of math class in like two years.
and that was algebra II and i didn't give a crap about it.

but i need to get back into stuff like this like i used to be. haha

This is amazing. I love math when it's in theories.

All I could think of during this video was Jade's, "and we spent the next 5 years on shrooms..."

Quote: Originally posted by MESinc.

All I could think of during this video was Jade's, "and we spent the next 5 years on shrooms..."

HAHA i know!!

Magnetic zeros? Hmm... Equations that are finite at the origin (x = 0) for non-negative integer α, and diverge as x approaches zero for negative non-integer α. The solution type (e.g., integer or non-integer).

This would look roughly like oscillating sine or cosine functions that decay proportionally to 1/√x , although their roots are not generally periodic, except asymptotically for large x. (J1(x) is the derivative of J0(x), much like − sin(x) is the derivative of cos(x).)

For integer orders α=0,1,2.
For non-integer α, the functions Jα(x) and J − α(x) are linearly independent, and are therefore the two solutions of the differential equation. On the other hand, for integer order α, the following relationship is valid (note that the Gamma function becomes infinite for negative integer arguments):[2]

This means that the two solutions are no longer linearly independent. In this case, the second linearly independent solution is then found to be the Bessel function of the second kind.

If you want to know when to use or apply your magnetic zero theroy:

1. You have a partial differential equation in cylindrical coordinates describing evolution in time of a quantity (in your case a concentration) that varies in the radial direction.
2. You proceed by assuming that the solution of the PDE can be expressed as an infinite sum of terms, each of which separates into a function of time only multiplied by a function of space only.
3. For each of the individual terms in this series, you obtain an ODE for the function of space only.
4. Incorporating suitable boundary conditions, the ODE becomes an eigenvalue problem.
5. There are countably many solutions of the eigenvalue problem (often numbered n=0,1,2,3,... for example) and the eigenfunctions are all mutually orthogonal.
6. You now have a bona fide infinite series, and return to the original PDE, incorporate the initial conditions, and use the orthogonality property to determine each of the coefficients that make the infinite series as a whole conform to the initial conditions.
7. The infinite series is the solution of your time-dependent problem.

jesus christ.

phobiac can do anything.

whu....